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Two pipes of same length and diameters d and 2d respectively are connected in series. The diameter of an equivalent pipe of same length is (a) Less than d (b) Between d and 1.5 d (c) Between 1.5 d and 2d (d) Greater than 2d Correct option is 'a'. Can any one explain?
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Two pipes of same length and diameters d and 2d respectively are conne...
Explanation:
When two pipes of the same length and different diameters are connected in series, the equivalent pipe is formed by joining the two pipes end to end. The equivalent pipe has the same length as the two individual pipes, but its diameter may vary.
Diameter of the first pipe: d
Diameter of the second pipe: 2d
To find the diameter of the equivalent pipe, we need to calculate the hydraulic radius (R) of each pipe using the formula:
R = (π * d^2) / (4 * A)
where A is the cross-sectional area of the pipe.
Hydraulic radius of the first pipe:
R1 = (π * d^2) / (4 * A1)
Hydraulic radius of the second pipe:
R2 = (π * (2d)^2) / (4 * A2)
= (π * 4d^2) / (4 * A2)
= (π * d^2) / A2
= 4 * R1 (since A2 = 4 * A1)
The total hydraulic radius of the equivalent pipe is the sum of the hydraulic radii of the individual pipes:
R_total = R1 + R2
= R1 + 4 * R1
= 5 * R1
Comparison:
Since R_total = 5 * R1, it means the hydraulic radius of the equivalent pipe is 5 times the hydraulic radius of the first pipe.
Now, let's compare the diameters of the first pipe (d) and the equivalent pipe (D):
D = 2 * √(R_total * A_total) / (π)
= 2 * √(5 * R1 * A_total) / (π)
= 2 * √(5 * R1 * (π * d^2) / 4) / (π)
= √(5 * d^2)
= d * √5
Conclusion:
From the above calculation, it is clear that the diameter of the equivalent pipe (D) is less than the diameter of the first pipe (d). Therefore, the correct option is (a) Less than d.
When two pipes of the same length and different diameters are connected in series, the equivalent pipe is formed by joining the two pipes end to end. The equivalent pipe has the same length as the two individual pipes, but its diameter may vary.
Diameter of the first pipe: d
Diameter of the second pipe: 2d
To find the diameter of the equivalent pipe, we need to calculate the hydraulic radius (R) of each pipe using the formula:
R = (π * d^2) / (4 * A)
where A is the cross-sectional area of the pipe.
Hydraulic radius of the first pipe:
R1 = (π * d^2) / (4 * A1)
Hydraulic radius of the second pipe:
R2 = (π * (2d)^2) / (4 * A2)
= (π * 4d^2) / (4 * A2)
= (π * d^2) / A2
= 4 * R1 (since A2 = 4 * A1)
The total hydraulic radius of the equivalent pipe is the sum of the hydraulic radii of the individual pipes:
R_total = R1 + R2
= R1 + 4 * R1
= 5 * R1
Comparison:
Since R_total = 5 * R1, it means the hydraulic radius of the equivalent pipe is 5 times the hydraulic radius of the first pipe.
Now, let's compare the diameters of the first pipe (d) and the equivalent pipe (D):
D = 2 * √(R_total * A_total) / (π)
= 2 * √(5 * R1 * A_total) / (π)
= 2 * √(5 * R1 * (π * d^2) / 4) / (π)
= √(5 * d^2)
= d * √5
Conclusion:
From the above calculation, it is clear that the diameter of the equivalent pipe (D) is less than the diameter of the first pipe (d). Therefore, the correct option is (a) Less than d.
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Two pipes of same length and diameters d and 2d respectively are connected in series. The diameter of an equivalent pipe of same length is (a) Less than d (b) Between d and 1.5 d (c) Between 1.5 d and 2d (d) Greater than 2d Correct option is 'a'. Can any one explain?
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Two pipes of same length and diameters d and 2d respectively are connected in series. The diameter of an equivalent pipe of same length is (a) Less than d (b) Between d and 1.5 d (c) Between 1.5 d and 2d (d) Greater than 2d Correct option is 'a'. Can any one explain? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Two pipes of same length and diameters d and 2d respectively are connected in series. The diameter of an equivalent pipe of same length is (a) Less than d (b) Between d and 1.5 d (c) Between 1.5 d and 2d (d) Greater than 2d Correct option is 'a'. Can any one explain? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes of same length and diameters d and 2d respectively are connected in series. The diameter of an equivalent pipe of same length is (a) Less than d (b) Between d and 1.5 d (c) Between 1.5 d and 2d (d) Greater than 2d Correct option is 'a'. Can any one explain?.
Two pipes of same length and diameters d and 2d respectively are connected in series. The diameter of an equivalent pipe of same length is (a) Less than d (b) Between d and 1.5 d (c) Between 1.5 d and 2d (d) Greater than 2d Correct option is 'a'. Can any one explain? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Two pipes of same length and diameters d and 2d respectively are connected in series. The diameter of an equivalent pipe of same length is (a) Less than d (b) Between d and 1.5 d (c) Between 1.5 d and 2d (d) Greater than 2d Correct option is 'a'. Can any one explain? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes of same length and diameters d and 2d respectively are connected in series. The diameter of an equivalent pipe of same length is (a) Less than d (b) Between d and 1.5 d (c) Between 1.5 d and 2d (d) Greater than 2d Correct option is 'a'. Can any one explain?.
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